Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions
Jim Rulla, Noel J. Walkington · SIAM Journal on Numerical Analysis · 1996
Fully discrete implicit schemes for the solution of degenerate parabolic equations in two dimensions are shown to satisfy error estimates of the form $O(\tau + \ln ({1 / h})^\alpha h)$, where $\tau $ is the time step size and h is the mesh size. These results apply to both the Stefan problem and the porous medium equation.